Question: Rewrite as a simplified fraction. ${0.\overline{82} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}100x &= 82.8282...\\ 1x &= 0.8282...\end{aligned}}$ Subtracting the two equations, we have: ${99x = 82}$ ${x = \dfrac{82}{99}} $